Method for calculating high-resolution wafer parameter profiles

ABSTRACT

An embodiment of the present invention provides a method to utilize data from many different die sizes and products so that highly detailed wafer profiles can be generated that have an improved signal to noise ratio and spatial resolution. Instead of being limited to single die size like normal wafer maps, this method takes advantage of multiple die sizes and their variation in placement on the wafer to increase the information available about the wafer patterns.

BACKGROUND OF THE INVENTION

The present invention generally relates to a method for calculatinghigh-resolution wafer parameter profiles.

Integrated circuit yields on wafers frequently follow patterns acrossthe wafer. Analysis of these patterns is useful in determining thesource of process variations or yield loss. An observed pattern can bematched against the physical characteristics of a process tool or thepatterns observed by other techniques such as particle inspections.

Typically, the wafer patterns are observed by plotting yields or someother parametric value of a specific device by die in what is known as awafer map. This is useful when working with obvious patterns that standout given the die size or number of data points available to be plotted.This approach has limited value when dealing with very large die or whenthere is limited data from a given product or when the impact isrelatively low compared to the background variation, i.e., a poor signalto noise ratio.

The typical approaches for generating wafer profiles are:

-   -   1) Stacking data from the die of many wafers of the same product        into what is known as a stacked wafer map;    -   2) Using data from the smallest die sized product in order to        have a higher spatial resolution; and    -   3) Using the data from methods 1 or 2 above to interpolate        values in between die locations through the use of statistical        smoothing algorithms. These results are sometimes known as        response surface plots or contour maps.

The foregoing approaches, however, are typically met with the followingproblems:

-   -   1) When using data from only one product there may be only a        limited number of data points per die location availed from that        product in the time frame of interest;    -   2) If the die size is relatively large for the selected product,        the spatial resolution will be poor and important patterns will        not be resolved; and    -   3) The accuracy of statistical interpolations using the above        data will be limited in accuracy based on the data used.

OBJECTS AND SUMMARY OF THE INVENTION

A primary object of an embodiment of the present invention is to providea method to utilize data from many different die sizes and products sothat highly detailed wafer profiles can be generated that have animproved signal to noise ration and spatial resolution.

Another primary object of an embodiment of the present invention is toprovide sufficient resolution of patterns that occur across the wafer.

An object of an embodiment of the present invention is to match waferyield patterns with physical wafer contact points in process equipmentin order to troubleshoot and improve the process or equipment.

Another object of an embodiment of the present invention is to adjustdie placement on the wafer in order to maximize yields.

Another object of an embodiment of the present invention is to matchwafer yield or electrical test patterns with etch clearing patterns,such as center last, to facilitate recipe optimization.

Yet another object of an embodiment of the present invention is toprovide better resolution of spatial patterns on a wafer than the datafrom any single product can provide.

Still another object of an embodiment of the present invention is thatnormalizing and smoothing across the multiple products provides a mapthat better represents the process-induced patterns as opposed to anyproduct specific pattern.

Another object of an embodiment of the present invention is that theabsolute physical coordinate system allows the data to be correlated tophysical causes and use as data for modeling.

Briefly, and in accordance with at least one of the foregoing objects,an embodiment of the present invention provides a method to utilize datafrom many different die sizes and products so that highly detailed waferprofiles can be generated that have an improved signal to noise ratioand spatial resolution. Instead of being limited to single die size likenormal wafer maps, this method takes advantage of multiple die sizes andtheir variation in placement on the wafer to increase the informationavailable about the wafer patterns.

BRIEF DESCRIPTION OF THE DRAWINGS

The organization and manner of the structure and operation of theinvention, together with further objects and advantages thereof, maybest be understood by reference to the following:

FIG. 1 illustrates a flow chart of a method for calculatinghigh-resolution wafer parameter profiles; and

FIG. 2 illustrates a top view of a die on a wafer.

DESCRIPTION

While the invention may be susceptible to embodiment in different forms,there is shown in the drawings, and herein will be described in detail,a specific embodiment with the understanding that the present disclosureis to be considered an exemplification of the principles of theinvention, and is not intended to limit the invention to that asillustrated and described herein.

In this invention, the die from many different products is used tocreate a high-resolution profile of the wafer. This is done byassociating die-based values to a standard grid based on the location ofthe die with respect to that grid. The procedure will work for anydie-based data such as yields, or electrical test values. It can also beapplied to wafer based measurements that are limited specific structureslocation in the wafer scribe area such as gate oxide thickness or linewidth measurements. The concept is that by using data from die ofdifferent sizes more information about the patterns on the wafers can bedetermined.

Thus, a method 100 for calculating high-resolution wafer parameterprofiles is illustrated in the flow chart of FIG. 1.

The method 100 includes step 102, which is to define appropriateproduct/device input dataset. The appropriate product/device inputdataset are defined by the following:

-   -   1. A variety of devices with die level data and different die        sizes;    -   2. Products/devices must represent the same process flow to be        modelled;    -   3. Sufficient number of lots from each device to calculate a        reasonable average result value for each die;    -   4. Die size for each device; and    -   5. At least one reference physical correlation point between a        specific virtual coordinate (i.e., row-column) and an actual        physical location on the wafer (e.g., center of wafer).

Table 1, for example, is a list of products used in the dataset definedby step 102. TABLE 1 List Of Products Used In Dataset Upper/LeftUpper/Left Corner Corner Chip Code Die X size Die Y size (64, 64) X (64,64) Y Status Note CD3B 5.703 5.775 −26.512 92.4 Used CD34 8.508 8.478−25.624 93.536 Used CP9B 10.743 10.716 −32.229 90.944 Used CP8Q 11.90711.88 −42.721 86.64 Used CP9R 5.808 5.976 −26.132 92.616 Used CD3Z13.734 13.38 −34.368 86.96 Used CL1L 6.654 6.627 −19.308 94.705 UsedCD3Y 15.135 14.478 −45.405 85.068 Used CPCB 3.603 2.973 −18.815 95.136Used CP0L 13.839 13.686 −34.578 87.402 Not Used Rotated AS0P 9.402 9.243−28.204 92.43 Not Used Rotated CD5A 8.283 8.283 −35.849 91.196 Not UsedOnly 3 Lots CD39 3.909 3.879 −17.536 95.275 Not Used Only 2 Lots

It should be noted that in Table 1, the upper/left corner x and ycolumns identify the physical location in millimeters of the top-leftcorner of the top-left die on a wafer for that product as referencedfrom the center of the wafer. Any reference coordinate method could beused as long as it makes a physical to virtual association and is usedconsistently across the devices.

The method 100 further includes step 104, which is to collect a dielevel dataset for one of the products/devices defined in step 102, seeTable 1, by generating a table of data for the lots and wafers of agiven product/device with the virtual die coordinate (i.e., row-column)for each die and its corresponding value (i.e., yield bin, parametricmeasurement, etc.).

Table 2, for example, is an example die level yield bin data for aproduct/device. TABLE 2 Example Die Level Yield Bin Data For AProduct/Device Bin # Bin # Bin # Bin # Index Row Index Column Lot 1:Wafer 1 Lot 1: Wafer 2 Lot 2: Wafer 1 Lot 2: Wafer 2 56 60 9 8 9 8 56 598 9 8 15 56 57 8 15 8 15 56 58 12 15 8 15 56 56 8 15 9 15 57 56 8 9 8 957 57 1 9 9 9 57 58 8 8 9 12 57 59 8 8 9 8 57 61 8 9 8 8 57 62 8 9 8 857 60 1 8 8 8 57 54 1 8 9 8 57 55 8 8 9 12 58 55 1 8 9 8 58 63 8 9 9 958 54 8 9 8 9 58 53 8 9 8 8 58 60 1 8 8 8

The method 100 further includes the step 106, which is to calculate asingle composite value for each die coordinate. This could be anaverage, max, sum, percentage, etc. of the data from all the individuallots and wafers corresponding die site. In the example in Table 3, thepercent of bin 1 die from each location was calculated. TABLE 3 ExampleComposite Value Data For Each Die Coordinate Index Row Index Column %Die Yield 93 26 0.057 93 −25 0.249 93 0 0.203 93 9 0.082 93 17 0.094 93−17 0.187 85 −42 0.315 85 −25 0.612 85 43 0.189 85 34 0.383 85 −34 0.49085 9 0.461 85 26 0.425 85 0 0.566

The method 100, further includes the step 108, which is to normalize thecomposite die values so that they can be merged with values from theother products, if necessary. For example, yields vary by product anddie size and cannot be used together without normalization. Anynormalization algorithm could be used (e.g., Poisson Defect Density,max-min scaling, etc.). In Table 4, a max-min scaling was used where therange of the yield was adjusted to scale from 0 to 1. TABLE 4 NormalizedValues Index Row Index Column % Die Yield % Norm Yield 93 26 0.057 0.06893 −25 0.249 0.296 93 0 0.203 0.242 93 9 0.082 0.098 93 17 0.094 0.11193 −17 0.187 0.223 85 −42 0.315 0.375 85 −25 0.612 0.728 85 43 0.1890.224 85 34 0.383 0.455 85 −34 0.490 0.583 85 9 0.461 0.549 85 26 0.4250.506 85 0 0.566 0.673

The method 100 further includes the step 110, which is to define whereon the virtual die it is desired to assign the composite value. Thelocation assignment depends on the purpose of the composite profile. Forexample, and as illustrated in FIG. 2, if it is believed that the valuebeing measured for each die is driven by its nearness to the edge 202 ofthe wafer 200, the value could be assigned to the corner 204 of the die206 nearest the edge 202 of the wafer 200. If, however, the purpose isto assess a mechanism stemming from the center 208 of the wafer 200, thevalue could assigned to the corner 210 of the die 206 nearest the center208 of the wafer 200. If, however, there is no specific mechanism inmind, the value could be associated with the center 212 of the die 206.

The method 100 further includes the step 112, which is to calculatephysical coordinates for each die value using the corresponding virtualcoordinate and physical translation key. Using the virtual to physicaltranslation key in the product information, Table 1, calculate aphysical point on which to associate the value for each virtual dielocation. TABLE 5 Physical Coordinates (X mm & Y mm) % Index Index IndexIndex % Die Norm Row Column X mm Y mm Yield Yield 93 26 10.5 2.5 0.0570.068 93 −25 10.5 −2.5 0.249 0.296 93 0 10.5 −0.5 0.203 0.242 93 9 10.50.5 0.082 0.098 93 17 10.5 1.5 0.094 0.111 93 −17 10.5 −1.5 0.187 0.22385 −42 9.5 −4.5 0.315 0.375 85 −25 9.5 −2.5 0.612 0.728 85 43 9.5 4.50.189 0.224 85 34 9.5 3.5 0.383 0.455 85 −34 9.5 −3.5 0.490 0.583 85 99.5 0.5 0.461 0.549 85 26 9.5 2.5 0.425 0.506 85 0 9.5 −0.5 0.566 0.673

Any coordinate system could be used (e.g., Cartesian, polar, etc.). Inthis example, a Cartesian coordinate system was used and the location isa combination of offset translations:XCoord=(wafer translation in x)+(column translation in x)+(dietranslation in x)YCoord=(wafer translation in y)+(row translation in y)+(die translationin y)

-   -   1. The wafer translation is given in the reference coordinate        from Table 1 (W_(x) and W_(y)).    -   2. The column translation is calculated as the number of columns        between the reference die and the die in question times the die        width (ΔC times D_(x)).    -   3. The row translation similarly is calculated as the number of        rows between the reference die and the die in question times the        die height (ΔR times D_(y)).    -   4. The die translation is the distance between the reference        point on the reference die and the position in the die where it        is desired to place the value in the die (DT_(x), DT_(y)). For        example, the value can be placed at the corner of the die        nearest the edge of the wafer, so a die in the upper right        quadrant would use the upper right corner of the die which is        one die width right of the reference die which is identified at        the upper left corner.

Thus:F _(x) =W _(x) +ΔC·D _(x) +DT _(x)andF _(y) =W _(y) +ΔR·D _(y)+0

The method 100 further includes step 114, which is to repeat steps 104,106, 108, 110 and 112 for each product defined in step 102, e.g., eachproduct used in Table 1.

The method 100 further includes step 116, which is to merge the datafrom all the files into one file. Thus, the various sized die will have“filled in” a large number of points on the wafer.

The method 100 further includes the step 118, which is to define a gridthat is at the resolution of needed for the analysis. This can vary insize. A typical size useful for integrated circuit manufacturingpurposes would be between 0.25 millimeters and 5 millimeters.

The method 100 further includes the step 120, which is to create a tablewith all the possible grid coordinates that would fit on a productionwafer. This requires defining any regions on the wafer where die cannotbe placed (e.g., title area, edge exclusion, clamp marks, etc.).

The method 100 further includes the step 122, which is to define asmoothing algorithm. The purpose of the smoothing algorithm is to usethe non-uniform data in the combined composite map to estimate apredicted value for every coordinate on the uniform grid map defined instep 118. For example, a distance weighted smoothing algorithm with aGaussian kernel to estimate each point could be used. Any smoothingalgorithm can be used depending on what is judged to give the bestestimate of the true value. The formula used, for example, is:$V_{x,y} = \frac{\sum\limits_{i = 1}^{n}{V_{i}*( {1 - ( {d/d_{\max}} )^{2}} )^{2}}}{\sum\limits_{i = 1}^{n}( {1 - ( {d/d_{\max}} )^{2}} )^{2}}$

-   -   V_(x,y) Is the smoothed value at location x,y    -   V_(i) Is the known value i from the composite product dataset    -   n Is the total number of values in the composite product dataset    -   d Is the Euclidean distance ((x−x_(i))²+(y−y_(i))²)^(1/2)    -   d_(max) Is a user setting to limit a value beyond a max distance        from affecting the smoothed average

The method 100 further includes the step 124, which is to calculate thesmoothed value for each point on the grid from the combined data. Table6 shows an example final data table of the smoothed data set, using theforegoing formula. TABLE 6 Smoothed Data Set Example Xmm Ymm SmoothedValue −1 82 0.850 −1 83 0.838 −1 84 0.826 −1 85 0.814 −1 86 0.801 −1 870.789 −1 88 0.776 −1 89 0.763 −1 90 0.752 −1 91 0.743 −1 92 0.734 −1 930.725 −1 94 0.716 −1 95 0.706 −1 96 0.698 −1 97 0.694 0 −93 0.226 0 −920.280 0 −91 0.337 0 −90 0.398 0 −89 0.466 0 −88 0.536 0 −87 0.606 0 −860.673 0 −85 0.734 0 −84 0.783 0 −83 0.816 0 −82 0.835

The method 100 further includes the step 126, which is to plot the waferprofile for various visualizations. For instance the wafer profile canbe scaled in equal increments of the range of values, which in this casetends to highlight the high variability of the edge values, or the waferprofile can be scaled in equal percentiles of the data, which betterhighlights the more subtle variability in the center of the wafer. Thewafer profile could also be plotted to show a three-dimensional contourmap of the data.

Thus, the method 100 provides a number of features, including thefollowing:

-   -   1. The use of die based data from multiple products of different        die sizes (resolutions) to create a higher resolution wafer        profile of the data;    -   2. Normalizing the data from the various die sizes so that they        can be combined into a larger data set for the same parameter;    -   3. Conversion of the data from a set of disjointed virtual        coordinate systems to a single physical coordinate system;    -   4. Applying smoothing or modeling algorithms to the        non-uniformly populated data set to fully populate a uniform        high-resolution grid;    -   5. The use of two-dimensional and three-dimensional plots to        visualize the patterns on the wafer;    -   6. The use of the high-resolution maps to correlate the spatial        patterns to manufacturing defect maps, and equipment        configurations, and wafer handling methods to identify process        improvement opportunities; and    -   7. The use of the high-resolution data table for other        optimization calculations such as die placement for yield or        auto-inking decisions for product quality improvement.

The method 100 also provides a number of advantages over the methods ofthe prior art, including:

-   -   1. Providing better resolution of spatial patterns on a wafer        than the data from any single product can provide;    -   2. Normalizing and smoothing across the multiple products        provides a map that better represents the process-induced        patterns as opposed to any product specific pattern; and    -   3. The absolute physical coordinate system allows the data to be        correlated to physical causes and use as data for modeling.

It should be noted that the method 100 could be run in a different orderthan as described hereinabove in order to achieve the same result insubstantially the same way. For example, the physical grid association(step 120) could be done before the product normalization (step 112) orthe data could be combined from different products (step 116) beforebeing normalized (step 108).

It should further be noted that instead of a grid, some other coordinatemethod could be used to get the same result with substantially the sameprocess, such as a polar coordinate system.

It should further be noted that any statistical smoothing algorithmcould be used to fill in the non-uniform data.

It should further be noted that the method 100 could be applied tosample based data collection where only some of the dies havemeasurements. For example, E-test or critical dimension data that onlytest certain sites on the wafer. Because of the product layoutdifferences the “same sites” on one product are actually in a slightlydifferent physical location from another product. There is a resulting“cloud” of data at every site that can increase spatial resolution.

Finally, it should further noted that the method 100 could be applied tovarious collections of data that are all on a physical coordinate systemnot necessarily associated with a die boundary. An example applicationof this would be for a tool supplier to collect test wafer measurementsfrom multiple fabs to determine a process profile with a larger datasetthan could be generated from a single factory.

While an embodiment of the present invention is shown and described, itis envisioned that those skilled in the art may devise variousmodifications of the present invention without departing from the spiritand scope of the appended claims.

1. A method for calculating high-resolution wafer parameter profilescomprising the steps of: a) defining appropriate product/device inputdataset; b) collecting a die level dataset for one of theproducts/devices defined in step (a) by generating a table of data forthe lots and wafers of said one product/device with the virtual diecoordinate for each die and its corresponding value; c) calculating asingle composite value for each die coordinate; d) defining where on thevirtual die it is desired to assign the composite value; e) calculatingphysical coordinates for each die value using the corresponding virtualcoordinate and physical translation key; f) repeating steps (b), (c),(d) and (e) for each product defined in step (a); g) merging the datafrom all the files into one file; h) defining a grid that is at theresolution of needed for the analysis; I) creating a table with all thepossible grid coordinates that would fit on a production wafer; j)defining a smoothing algorithm; k) calculating the smoothed value foreach point on the grid from the combined data; and l) plotting the waferprofile for various visualizations.
 2. A method as defined in claim 1,further including the step of normalizing the composite die values sothat they can be merged with values from the other products.
 3. A methodas defined in claim 2, wherein a Poisson Defect Density normalizingalgorithm is used to perform the step of normalizing the composite dievalues so that they can be merged with values from the other products.4. A method as defined in claim 2, wherein a max-min scaling normalizingalgorithm is used to perform the step of normalizing the composite dievalues so that they can be merged with values from the other products.5. A method as defined in claim 1, wherein said appropriateproduct/device input dataset of step (a) are defined by a variety ofdevices with die level data and different die sizes.
 6. A method asdefined in claim 1, wherein said appropriate product/device inputdataset of step (a) are defined by products/devices which represent thesame process flow to be modeled.
 7. A method as defined in claim 1,wherein said appropriate product/device input dataset of step (a) aredefined by sufficient number of lots from each device to calculate areasonable average result value for each die.
 8. A method as defined inclaim 1, wherein said appropriate product/device input dataset of step(a) are defined by die size for each device.
 9. A method as defined inclaim 1, wherein said appropriate product/device input dataset of step(a) are defined by at least one reference physical correlation pointbetween a specific virtual coordinate and an actual physical location onthe wafer.
 10. A method as defined in claim 1, wherein said calculatedsingle composite value for each die coordinate from step (c) is anaverage of the data from all the individual lots and waferscorresponding die site.
 11. A method as defined in claim 1, wherein saidcalculated single composite value for each die coordinate from step (c)is a max of the data from all the individual lots and waferscorresponding die site.
 12. A method as defined in claim 1, wherein saidcalculated single composite value for each die coordinate from step (c)is a sum of the data from all the individual lots and waferscorresponding die site.
 13. A method as defined in claim 1, wherein saidcalculated single composite value for each die coordinate from step (c)is a percentage of the data from all the individual lots and waferscorresponding die site.
 14. A method as defined in claim 1, wherein saidcomposite value from step (d) is assigned to a corner of the die nearestan edge of the wafer.
 15. A method as defined in claim 1, wherein saidcomposite value from step (d) is assigned to a corner of the die nearesta center of the wafer.
 16. A method as defined in claim 1, wherein saidcomposite value from step (d) is assigned from a center of the die. 17.A method as defined in claim 1, wherein a Cartesian coordinate system isused to calculate physical coordinates from step (e).
 18. A method asdefined in claim 1, wherein a polar coordinate system is used tocalculate physical coordinates from step (e).
 19. A method as defined inclaim 1, wherein the wafer profile is scaled, in accordance with step(l), in equal increments of the range of values.
 20. A method as definedin claim 1, wherein the wafer profile is scaled, in accordance with step(l), in equal percentiles of the data.
 21. A method as defined in claim1, wherein the wafer profile is plotted, in accordance with step (l), toshow a three-dimensional contour map of the data.